Question 1

Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 7 and the interval [a, x] = [6, x].

Accepted Answer

A)  7(x - 6) 
B)  7(x + 6) 
C)  7x 
D)  42 
E)  7

Question 2

Evaluate  .

Accepted Answer

The answer of Evaluate  ....

Question 3

Answer true or false. The area between y = x7 + cos x and the x-axis on [0, 5] is  .

Accepted Answer

A) True 
 B)False

Question 4

Express the antiderivative of  on the interval (-$\infty$,+$\infty$) as an integral, F(x), whose value at x = -3 is 0.

Accepted Answer

The answer of Express the antiderivative of  on the...

Question 5

Find the position at time t = 3 second of a particle if v(t) = 4t - 6; s = 8 when t = 0.

Accepted Answer

The answer of Find the position at time t =...

Question 6

Answer true or false.

Accepted Answer

A) True 
 B)False

Question 7

Given f(x) = 7 + x . Use the rectangle method to approximate the area on the interval [0, 3] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Accepted Answer

The answer of Given f(x) = 7 + x ....

Question 8

Find y(x) if  and y(0) = 1.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Find the average value of f(x) = (x + 1)² over [-1, 2]. Approximate value to three decimal places.

Accepted Answer

The answer of Find the average value of f(x) =...

Question 10

Find the displacement of a particle if v(t) = t⁴ + 4; [0, 5].

Accepted Answer

The answer of Find the displacement of a particle if...

Question 11

Evaluate  .

Accepted Answer

The answer of Evaluate  ....

Question 12

Answer true or false.  .

Accepted Answer

A) True 
 B)False

Question 13

Find the average value of  for  .

Accepted Answer

The answer of Find the average value of  for...

Question 14

Evaluate  .

Accepted Answer

The answer of Evaluate  ....

Question 15

Simplify. ln(e - 7x ) =

Accepted Answer

A)  7 
B)  x-7 
C)  -7 
D)  x7 
E)  -7x

Question 16

A projectile fired upward from the ground is to reach 144 feet. What must be its initial velocity?

Accepted Answer

The answer of A projectile fired upward from the ground...

Question 17

Evaluate

Accepted Answer

The answer of Evaluate ...

Question 18

Evaluate the integral by making the indicated substitution. , u = x⁴ .

Accepted Answer

The answer of Evaluate the integral by making the indicated...

Question 19

A particle is moving so that its velocity, v(t) = t² -3t - 10 for 0 $\le$ t $\le$ 7. Find the total distance travelled by the particle.

Accepted Answer

The answer of A particle is moving so that its...

Question 20

Evaluate  if  .

Accepted Answer

The answer of Evaluate  if  ....

Exam 5: Integration

Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 7 and the interval [a, x] = [6, x].

Evaluate .

Answer true or false. The area between y = x⁷ + cos x and the x-axis on [0, 5] is .

Express the antiderivative of $Express the antiderivative of on the interval (- \infty ,+ \infty ) as an integral, F(x), whose value at x = -3 is 0.$ on the interval (- $\infty$ ,+ $\infty$ ) as an integral, F(x), whose value at x = -3 is 0.

Find the position at time t = 3 second of a particle if v(t) = 4t - 6; s = 8 when t = 0.

Answer true or false.

Given f(x) = 7 + x . Use the rectangle method to approximate the area on the interval [0, 3] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Find y(x) if and y(0) = 1.

Find the average value of f(x) = (x + 1)² over [-1, 2]. Approximate value to three decimal places.

Find the displacement of a particle if v(t) = t⁴ + 4; [0, 5].

Evaluate .

Answer true or false. .

Find the average value of for .

Evaluate .

Simplify. ln(e ^- ⁷^x ) =

A projectile fired upward from the ground is to reach 144 feet. What must be its initial velocity?

Evaluate

Evaluate the integral by making the indicated substitution. , u = x⁴ .

A particle is moving so that its velocity, v(t) = t² -3t - 10 for 0 $\le$ t $\le$ 7. Find the total distance travelled by the particle.

Evaluate if .

Exam 5: Integration

Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 7 and the interval [a, x] = [6, x].

Evaluate .

Answer true or false. The area between y = x7 + cos x and the x-axis on [0, 5] is .

Express the antiderivative of on the interval (- ∞\infty∞ ,+ ∞\infty∞ ) as an integral, F(x), whose value at x = -3 is 0.

Find the position at time t = 3 second of a particle if v(t) = 4t - 6; s = 8 when t = 0.

Answer true or false.

Given f(x) = 7 + x . Use the rectangle method to approximate the area on the interval [0, 3] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Find y(x) if and y(0) = 1.

Find the average value of f(x) = (x + 1)2 over [-1, 2]. Approximate value to three decimal places.

Find the displacement of a particle if v(t) = t4 + 4; [0, 5].

Evaluate .

Answer true or false. .

Find the average value of for .

Evaluate .

Simplify. ln(e - 7x ) =

A projectile fired upward from the ground is to reach 144 feet. What must be its initial velocity?

Evaluate

Evaluate the integral by making the indicated substitution. , u = x4 .

A particle is moving so that its velocity, v(t) = t2 -3t - 10 for 0 ≤\le≤ t ≤\le≤ 7. Find the total distance travelled by the particle.

Evaluate if .

Answer true or false. The area between y = x⁷ + cos x and the x-axis on [0, 5] is .

Express the antiderivative of $Express the antiderivative of on the interval (- \infty ,+ \infty ) as an integral, F(x), whose value at x = -3 is 0.$ on the interval (- $\infty$ ,+ $\infty$ ) as an integral, F(x), whose value at x = -3 is 0.

Find the average value of f(x) = (x + 1)² over [-1, 2]. Approximate value to three decimal places.

Find the displacement of a particle if v(t) = t⁴ + 4; [0, 5].

Simplify. ln(e ^- ⁷^x ) =

Evaluate the integral by making the indicated substitution. , u = x⁴ .

A particle is moving so that its velocity, v(t) = t² -3t - 10 for 0 $\le$ t $\le$ 7. Find the total distance travelled by the particle.